Figure 3.

Spatial resolution. (A) A magnetic bead (4.5 μm diameter) and a magnetic cylinder (6 μm diameter) in dipolar interaction in a horizontal magnetic field of 20 mT. The white spot at the center of the bead (in red on the bottom image) is used to determine its position. The blue square is the region of interest used for image correlation on the cylinder (4 × 2.5 μm ²). Position of the cylinder measured with image correlation (a) and of the bead measured with the center of mass of the center spot (b), while enduring brownian fluctuations (x-axis 30 frames/s). The position of the bead is shifted by + 1 μm for better comparison. (c) Difference in the position determination of the bead and the cylinder with the two methods (center determination and image correlation, equivalent to the difference from the red and blue curve from (a) and (b)). Note that the scale is much smaller for the difference (c) (1/20). The mean difference is less than 1/20th of a pixel corresponding to 2.5 nm and giving an upper bound to the resolution of the two independent methods of position measurements. (B) (a) A magnetic cylinder (8 μm diameter) and several magnetic beads (Dynabeads my-one, 1.05 μm diameter) in dipolar interaction; the rectangle square is the limit of the zoomed part on (c), whose dimensions are 13 × 5.5 μm ². (b) A rough estimation of the position of the cylinder’s vertical surface is done by a threshold on grey level contrast measured on the green line of image (a). (c) and (d) Calibration of the estimation by using the chain of beads on the left part of the image whose position can be accurately determined. $\mathit{\phi }$ is the diameter of the small beads.